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Mission impossible (Posted on 2013-04-03) Difficulty: 2 of 5
In a certain football contest the winner scores 3 points, the loser 0, and in the case of a draw each team scores 1 point.

Out of all "possible" final scores (0<R<3*n) for a team, participating in N games, how many final results cannot be achieved?

See The Solution Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

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Solution Not achieved (spoiler) | Comment 1 of 5
(I want to say the answer is zero since if a score cannot be achieved it is not possible.  But I know this isn't what you mean.   I don't remember this problem from the queue or I'd have suggested a rewrite.)

The answer is 1.  For N games the only unachievable score is 3N-1.

Numbers of the form 3m can be (W,L,D) = (m,N-m,0)
Numbers of the form 3m+1 can be (m,N-m-1,1)
Numbers of the form 3m+2 can be (m,N-m-2,2) except where
there is only 1 non-win.  In that case there cannot be 2 draws.

  Posted by Jer on 2013-04-03 11:32:42
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